Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)
If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.
On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.
For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.
Then the range of F(x) is the interval [-π, π].
Answer:
x = -5
Step-by-step explanation:
Simplifying
6x + -3(x + -8) = 9
Reorder the terms:
6x + -3(-8 + x) = 9
6x + (-8 * -3 + x * -3) = 9
6x + (24 + -3x) = 9
Reorder the terms:
24 + 6x + -3x = 9
Combine like terms: 6x + -3x = 3x
24 + 3x = 9
Solving
24 + 3x = 9
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-24' to each side of the equation.
24 + -24 + 3x = 9 + -24
Combine like terms: 24 + -24 = 0
0 + 3x = 9 + -24
3x = 9 + -24
Combine like terms: 9 + -24 = -15
3x = -15
Divide each side by '3'.
x = -5
Hope this Helps
I hope this is correct
Hey there!
Your answer is C.
If you take the lengths of the legs of the triangle, which are 12 and 4, we can multiply them by the scale factor to see what the legs of our new triangle is.
12 x 1/4 = 3
4 x 1/4 = 1
So, the legs of our new triangle have lengths of 1 and 3.
We can see that option C has the correct triangle in red.
If we're looking at the ratio of rise to run of each triangle, it is 1/3 for both the large triangle and the small triangle.
The rise for the larger triangle is 4, and the run is 12. That is 4/12, which can be simplified to 1/3.
The rise for the smaller triangle is 1, and the run is 3. That is 1/3, which is all the way simplified already.
These triangles are similar because the first one was dilated to get the second one, which explains why the ratios are the same.
Hope this helps!
Patty because she has the lowest time out of them all. From least to greatest Patty would be the least with her time being shorter than the rest